With the Easter Holiday coming up, Wally World wants to choose an order quantity

Question

With the Easter Holiday coming up, Wally World wants to choose an order quantity for giant chocolate bunnies that will maximize their expected profit. Their expected demand follows a normal distribution with a mean of 3000 bunnies and a standard deviation of 500 bunnies. Each giant chocolate bunny costs $2.50 and can be sold for S9.00. Unsold giant chocolate bunnies will be marked down to S1.00. a. How many giant chocolate bunnies should Wally World order for the upcoming b. What is the in-stock probability if Wally World orders 4000 giant chocolate c. What is the stock-out probability if Wally World orders 3500 giant chocolate d. How many would wally world have to order to achieve a 99% in stock probability? Easter Holiday season? bunnies? bunnies?

Explanation / Answer

Given are following data on chocolate :

Price of chocolate = P = $9 / unit

Cost of chocolate = C = $2.5/ unit

Salvage price = S = $1/ unit

Therefore,

Underage cost ( Cu ) = P – C = $ 9 - $2,5 = $6.5

Overage cost ( Co ) = C – S = $2.5 - $1 = $1.5

Therefore , Critical ratio = Cu/ ( Cu = Co) = 6.5/(6.5 + 1.5) = 6.5/8 = 0.8125

Critical ratio is the probability of optimum order quantity.

Therefore, probability of the optimum order quantity = 0.8125

Corresponding Z value for probability of 0.815 = NORMSINV ( 0.8125 ) = 0.887

= Mean demand + Z x Standard deviation of demand

= 3000 + 0.887 x 500

= 3000 + 443.5

= 3443.5 ( 3444 rounded to next higher whole number )

3444 NUMBER OF CHOCOLATE BUNNIES SHOULD BE ORDERED

Therefore ,

3000 + Z1 x500 = 4000

Or, 500.Z1 = 1000

Or, Z1 = 2

Probability for Z1 = 2 as derived from standard normal distribution table is 0.97725

Therefore, instock probability = 0.97725

IN STOCK PROBABILITY = 0.97725

Therefore ,

3000 + Z1 x500 = 3500

Or, 500.Z1 = 500

Or, Z1 = 1

Probability for Z1 = 1 as derived from standard normal distribution table is 0.84134

Therefore , in stock probability = 0.84134

STOCKOUT PROBABILITY = 0.15866

Quantity Willy world needs to order

= Mean demand + z value x Standard deviation of demand

= 3000 + 2.326 x 500

= 3000 + 1163

= 4163

QUANTITY WILLY WORLD NEEDS TO ORDER = 4163 BUNNIES

3444 NUMBER OF CHOCOLATE BUNNIES SHOULD BE ORDERED

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